A374678 - OEIS

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A374678

Number of integer compositions of n whose leaders of maximal anti-runs are not distinct.

0, 0, 1, 1, 3, 7, 15, 32, 70, 144, 311, 653, 1354, 2820, 5850, 12054, 24810, 50923, 104206, 212841, 433919, 882930, 1793810, 3639248, 7373539, 14921986

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OFFSET

0,5

COMMENTS

The leaders of maximal anti-runs in a sequence are obtained by splitting it into maximal consecutive anti-runs (sequences with no adjacent equal terms) and taking the first term of each.

LINKS

Table of n, a(n) for n=0..25.

Gus Wiseman, Sequences counting and ranking compositions by their leaders (for six types of runs).

EXAMPLE

The anti-runs of y = (1,1,2,2) are ((1),(1,2),(2)) with leaders (1,1,2) so y is counted under a(6).

The a(0) = 0 through a(6) = 15 compositions:

. . (11) (111) (22) (113) (33)

(112) (221) (114)

(1111) (1112) (222)

(1121) (1113)

(1211) (1122)

(2111) (1131)

(11111) (1311)

(2211)

(3111)

(11112)

(11121)

(11211)

(12111)

(21111)

(111111)

MATHEMATICA

Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], !UnsameQ@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]

CROSSREFS

For constant runs we have A335548, complement A274174, ranks A374249.

The complement is counted by A374518, ranks A374638.

For weakly increasing runs we have complement A374632, ranks A374768.

Compositions of this type are ranked by A374639.

For identical instead of distinct leaders we have A374640, ranks A374520, complement A374517, ranks A374519.

A003242 counts anti-runs, ranks A333489.

A065120 gives leaders of standard compositions.

A106356 counts compositions by number of maximal anti-runs.

A238279 counts compositions by number of maximal runs

A274174 counts contiguous compositions, ranks A374249.

Cf. A034296, A188920, A189076, A238343, A239955, A333213, A373949, A374515.

Sequence in context: A026745 A139333 A099444 * A132402 A137166 A101890

Adjacent sequences: A374675 A374676 A374677 * A374679 A374680 A374681

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2024

STATUS

approved